penny - Anytime Dining follows the same dress code as Traditional Dining. On Princess you have Resort Casual and Formal Nights for dress. On your Princess Patter it will tell you what the dress code for the evening will be..
Its a really good idea to make reservations if you want to dine at peak dinner hours using Anytime Dining and its a good idea to make reservations for formal nights. If you don't make reservations and have to wait you will be given a pager. Go to the bar have a drink and then report to the dining room when your pager goes off. If you find a wait team that you really like you can request to be seated in their section.